It was not the Parkhead roar that beat Barcelona, but tactics that were played out to perfection

It was atmosphere this, fans that. The passion, noise and spectacle generated by their supporters always have been the essence of how Celtic home games are perceived in the Champions League. Barcelona have been as susceptible to that as the rest and over the past 36 hours a string of their players used Twitter or the Spanish media to cheerfully acknowledge the buffeting their senses took in Glasgow.

Even Celtic supporters may be blasé about all of this by now, however nice it is to hear that Lionel Messi and Andres Iniesta were impressed by what they experienced. Incredible volume and fanatical engagement from first to last are guaranteed on a major European night and that has helped Celtic to some inspirational results against Juventus, Barcelona (in 2004), Manchester United and AC Milan. But if the club is to grow in the Champions League it has to be about more than that, more than 1967, and the novelty of 60,000 fans screaming themselves hoarse. Wednesday showed Celtic can bring more to the great Uefa tournament. It was not the atmosphere that inflicted Barcelona's first loss in an away group game since defeat by Chelsea, more than six years ago.

Barcelona were not remotely rattled by Parkhead. In what felt like the aeon between Messi's stoppage-time goal and the final whistle, their passing, probing and movement were as intricate and composed as if working out balletic exchanges on a quiet training ground.

What makes Celtic's victory all the more admirable – for the club in general and manager Neil Lennon in particular – was that the players delivered a display which meant the supporters were not the only story. Their performance was intelligent and bold. Celtic are not good enough to prevent Barcelona dominating possession – no-one is – but they were good enough to stop them doing too much with it. At no point had Lennon written off as lost causes the two Barcelona games in Group G. He came within seconds of snatching a point at Camp Nou and went a step further at Parkhead.

Lennon had carefully watched DVDs of Barcelona. Their zonal marking at corners left little Jordi Alba exposed at the back post, he spotted. What if a pinpoint Charlie Mulgrew delivery was met by a towering Victor Wanyama header? What if, indeed. The hardest part was getting upfield to win a corner in the first place, but after 21 minutes Celtic did so and they scored.

Bringing an 18-year-old striker off the bench, while keeping Georgios Samaras, Miku Fedor and Kris Commons on the pitch, was brave. Lennon figured Tony Watt's pace and strength could trouble Barcelona on the counter-attack and that turned out to be another shrewd call. The game-plan worked because Lennon called things correctly and the players executed their chances perfectly. Watt capitalised on Xavi's error to score a stunning second goal.

The only way to beat Barcelona is to work tirelessly, tackle and deny them space through the middle – exhausting when the opposition controls nearly all the movement – then counter-attack with precision and strength. Those counters must yield a goal or a free-kick; set-pieces can expose Barcelona's lack of height in defence. Yes, Barcelona missed Carles Puyol and Gerard Pique but they have been out for a while and Real Madrid are the only other team to have beaten them this season. It is not as simple as Celtic's goals made it look.

It was a coaching vindication for Lennon and a profoundly satisfying result for Celtic. Financial prudence, highly accomplished scouting and recruitment, and admirable man-management drew out a terrific team performance and outstanding contributions by Wanyama, Fraser Forster, Adam Matthews and Watt.

The club can indulge itself with the fun of debating where the victory should be placed in its 125-year history. Second only to Lisbon was a common view yesterday although there may be a more sober assessment after the euphoria has ebbed away. It was a magnificent result which any club in Europe would envy. It was also a home fixture in the group stage against an opponent who did not need three points to qualify. Some mild criticism seemed to be coming at coach Tito Vilanova from the Spanish media afterwards for having too many small players in the Barcelona team. If the defeat had been in three or four months' time and knocked them out of the tournament the inquest would be far, far bloodier.

Lennon must feel he is in a different world, or at least in a different job. How small some elements of Scottish football must have seemed in the chaotic aftermath of Wednesday. Testing himself in the Champions League has allowed him to grow as a manager and to enjoy immersing himself in football issues and challenges rather than the tedious circus of relentless Old Firm pointscoring. In a throwaway line in his post-match press conference he referred to Watt being signed "from a club called Airdrie". He phrased it thus as he knew he was speaking to Spanish, English and other international reporters rather than just the same old local faces.

Celtic's win generated headlines and social media attention across the world. It was a level of fuss Lennon had never known, bigger than any Old Firm result. He was conspicuously measured and calm when he faced the media and even that felt like an attempt to send out a message. He wants Celtic to be a respected and familiar presence in the Champions League, not a club which looks beside itself with joy and disbelief at beating Barcelona. He did not want it to come across as some sort of freakish David and Goliath act. What did he really feel? Minutes earlier he had been leaping and hugging his team and backroom staff in the privacy of the dressing room, beaming from ear to ear.

Lennon wanted to bring the thunder back to Parkhead and he has done that. What is more impressive, when all the noise has died down, is the quiet substance of this Celtic manager and the team he has built.